{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Case study\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *\n",
    "\n",
    "from pandas import read_html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exponential, geometric, and polynomial growth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  Suppose there are two banks across the street from each other, The First Geometric Bank (FGB) and Exponential Savings and Loan (ESL).  They offer the same interest rate on checking accounts, 3%, but at FGB, they compute and pay interest at the end of each year, and at ESL they compound interest continuously.\n",
    "\n",
    "If you deposit $p_0$ dollars at FGB at the beginning of Year 0, the balanace of your account at the end of Year $n$ is\n",
    "\n",
    "$ x_n = p_0 (1 + \\alpha)^n $\n",
    "\n",
    "where $\\alpha = 0.03$.  At ESL, your balance at any time $t$ would be\n",
    "\n",
    "$ x(t) = p_0 \\exp(\\alpha t) $\n",
    "\n",
    "If you deposit \\$1000 at each back at the beginning of Year 0, how much would you have in each account after 10 years?\n",
    "\n",
    "Is there an interest rate FGB could pay so that your balance at the end of each year would be the same at both banks?  What is it?\n",
    "\n",
    "Hint: `modsim` provides a function called `exp`, which is a wrapper for the NumPy function `exp`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "p_0 = 1000\n",
    "alpha = 0.03"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "ts = linrange(11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1000.        , 1030.        , 1060.9       , 1092.727     ,\n",
       "       1125.50881   , 1159.2740743 , 1194.05229653, 1229.87386542,\n",
       "       1266.77008139, 1304.77318383, 1343.91637934])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "geometric = p_0 * (1 + alpha) ** ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1000.        , 1030.45453395, 1061.83654655, 1094.17428371,\n",
       "       1127.49685158, 1161.83424273, 1197.21736312, 1233.67805996,\n",
       "       1271.24915032, 1309.96445073, 1349.85880758])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "exponential = p_0 * exp(alpha * ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.030454533953516938"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "alpha2 = exp(alpha) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1000.        , 1030.45453395, 1061.83654655, 1094.17428371,\n",
       "       1127.49685158, 1161.83424273, 1197.21736312, 1233.67805996,\n",
       "       1271.24915032, 1309.96445073, 1349.85880758])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "geometric = p_0 * (1 + alpha2) ** ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "plot(ts, exponential, '-', label='Exponential')\n",
    "plot(ts, geometric, 's', label='Geometric')\n",
    "\n",
    "decorate(xlabel='Time (years)',\n",
    "         ylabel='Value (dollars)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Suppose a new bank opens called the Polynomial Credit Union (PCU).  In order to compete with First Geometric Bank and Exponential Savings and Loan, PCU offers a parabolic savings account where the balance is a polynomial function of time:\n",
    "\n",
    "$ x(t) = p_0 + \\beta_1 t + \\beta_2 t^2 $\n",
    "\n",
    "As a special deal, they offer an account with $\\beta_1 = 30$ and $\\beta_2 = 0.5$, with those parameters guaranteed for life.\n",
    "\n",
    "Suppose you deposit \\$1000 at all three banks at the beginning of Year 0.  How much would you have in each account at the end of Year 10?  How about Year 20?  And Year 100?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "number_of_years = 100\n",
    "ts = linrange(number_of_years+1)\n",
    "geometric = p_0 * (1 + alpha2) ** ts\n",
    "exponential = p_0 * exp(alpha * ts)\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "beta1 = 30\n",
    "beta2 = 0.5\n",
    "parabolic = p_0 + beta1 * ts + beta2 * ts**2\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def plot_results():\n",
    "    plot(ts, exponential, '-', label='Exponential')\n",
    "    plot(ts, geometric, 's', label='Geometric')\n",
    "    plot(ts, parabolic, 'o', label='Parabolic')\n",
    "    \n",
    "    decorate(xlabel='Time (years)',\n",
    "             ylabel='Value (dollars)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "plot_results()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "plot_results()\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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